Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `15`, `16`, and `12`?

Answer 1

`Area=85.45137` square units

Explanation:

Heron's formula for finding area of the triangle is given by
`Area=sqrt(s(s-a)(s-b)(s-c))`

Where `s` is the semi perimeter and is defined as
`s=(a+b+c)/2`

and `a, b, c` are the lengths of the three sides of the triangle.

Here let `a=15, b=16` and `c=12`

`implies s=(15+16+12)/2=43/2=21.5`

`implies s=21.5`

`implies s-a=21.5-15=6.5, s-b=21.5-16=5.5 and s-c=21.5-12=9.5`
`implies s-a=6.5, s-b=5.5 and s-c=9.5`

`implies Area=sqrt(21.5*6.5*5.5*9.5)=sqrt7301.9375=85.45137` square units

`implies Area=85.45137` square units